In recent years, the widespread adoption of lithium-ion batteries in electric vehicles, aerospace, and consumer electronics has highlighted their critical role in modern energy storage systems. These batteries offer high energy density, low self-discharge rates, and long cycle life, making them indispensable for sustainable technologies. However, a significant challenge lies in their degradation over repeated charge-discharge cycles. During operation, the capacity of a li ion battery gradually declines due to factors like lithium plating and solid electrolyte interphase (SEI) growth. This decay often follows a nonlinear trajectory: after an initial period of slow decline, a sudden acceleration occurs, known as the “knee point.” Beyond this point, the li ion battery experiences rapid capacity fade, potentially leading to safety hazards such as internal short circuits, thermal runaway, or even explosions. Therefore, accurately predicting both the cycle life and knee points of li ion batteries is essential for proactive health management, optimizing performance, and ensuring system safety. This need drives the development of advanced data-driven methods that can leverage raw operational data to forecast degradation without relying on complex electrochemical models.
Traditional approaches to li ion battery life prediction fall into model-based and data-driven categories. Model-based methods require detailed knowledge of internal mechanisms, which can be difficult to generalize across different battery types and operating conditions. In contrast, data-driven techniques extract patterns directly from historical data, offering greater flexibility and robustness. Recent studies have employed machine learning algorithms like support vector machines (SVM) and neural networks for this purpose. For instance, some researchers manually design health indicators (HIs) from discharge curves, but this process can be cumbersome and subjective. Deep learning methods, such as convolutional neural networks (CNN) and long short-term memory (LSTM) networks, automate feature extraction, capturing intricate nonlinear relationships in data. However, most existing models focus solely on cycle life prediction, neglecting the knee point—a critical transition that signals accelerated aging. Few works address knee point prediction, and those that do often depend on handcrafted features or assume specific degradation models, limiting their accuracy and applicability. To bridge this gap, I propose a multi-scale feature fusion model, termed MCNN-LSTM, which integrates CNNs with varying dilation rates and LSTMs to automatically learn features from raw voltage, current, and temperature (V/I/T) data. This model not only predicts the total cycle life of a li ion battery but also identifies the knee point early in its lifespan, enabling timely interventions and improved battery management strategies.
The core of my approach lies in leveraging multi-scale temporal features from li ion battery operational data. During discharge, parameters like voltage, current, and temperature evolve over time, reflecting the battery’s internal state. By analyzing these signals at different scales, I can capture both short-term fluctuations and long-term trends associated with degradation. For example, voltage curves shift leftward as capacity fades, while incremental capacity (IC) peaks diminish in height and area, indicating loss of active materials. Temperature profiles also show distinct patterns during charge and discharge cycles, with peaks correlating with energy dissipation. To formalize this, I represent the input data as a tensor for each li ion battery sample: let \( \mathbf{x}_i = (V_i, I_i, T_i) \in \mathbb{R}^{H \times W \times D} \), where \( H \) is the number of time samples per cycle (set to 80), \( W \) is the window length or number of cycles (e.g., 80 cycles), and \( D = 3 \) for the three data channels. This tensor serves as input to the MCNN-LSTM model, which consists of parallel branches for multi-scale feature extraction.
The MCNN-LSTM architecture combines three CNNs with different dilation rates and three LSTMs to process the V/I/T data. Dilation in CNNs allows for capturing features at varying temporal resolutions without increasing parameters significantly. For a one-dimensional convolution operation on a sequence \( s \), the output at position \( t \) with dilation rate \( r \) is given by:
$$ y_t = \sum_{k=0}^{K-1} w_k \cdot s_{t – r \cdot k} + b $$
where \( w_k \) are the filter weights, \( K \) is the kernel size, and \( b \) is the bias. By setting dilation rates to 1, 2, and 4, the CNNs extract features from immediate, medium, and long-range time dependencies, respectively. These features are then passed to LSTM networks, which model sequential dependencies through their gating mechanisms. The LSTM update equations for a time step \( t \) are:
$$ f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) $$
$$ i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) $$
$$ \tilde{C}_t = \tanh(W_C \cdot [h_{t-1}, x_t] + b_C) $$
$$ C_t = \tilde{C}_t \cdot i_t + C_{t-1} \cdot f_t $$
$$ o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) $$
$$ h_t = \tanh(C_t) \cdot o_t $$
Here, \( f_t \), \( i_t \), and \( o_t \) are the forget, input, and output gates; \( C_t \) is the cell state; \( h_t \) is the hidden state; and \( \sigma \) denotes the sigmoid function. The LSTMs capture long-term dependencies in the features extracted by CNNs, enhancing the model’s ability to track degradation trends. Additionally, a fully connected (FC) layer is used to learn linear combinations of features. The outputs from all branches are fused through an exponential linear unit (ELU) activation function, defined as \( \text{ELU}(x) = \max(0, x) + \min(0, \alpha(e^x – 1)) \) with \( \alpha = 0.1 \), which introduces nonlinearity while mitigating vanishing gradients. The final output layer produces predictions for cycle life and knee point. This multi-scale fusion ensures that the model leverages both local and global patterns in li ion battery data, improving prediction accuracy.
To train and evaluate the model, I use the Stanford-MIT dataset, which comprises aging tests on 124 commercial LFP/graphite li ion batteries. After filtering out anomalous data, 108 batteries are retained, with variations in cycle life due to manufacturing differences and charging protocols. The dataset is split into training (44 batteries), validation (32 batteries), and test (32 batteries) sets, ensuring a balanced representation of lifespan ranges. Input features are normalized using Min-Max scaling to accelerate convergence. For each li ion battery, I consider the first \( W \) cycles (with \( W \) tested as 40, 60, and 80) as input to predict the total cycle life, defined as the number of cycles until capacity drops to 80% of the nominal value. The knee point is identified post-hoc by fitting linear regressions to early and late degradation segments and finding their intersection, as described later. During training, I employ a sliding window technique to generate samples, with batch size set to 64 and the Adam optimizer (learning rate 0.001) over 2000 epochs. Dropout (rate 0.3) in LSTM layers prevents overfitting.
The performance of the MCNN-LSTM model is assessed using root mean square error (RMSE) and mean absolute percentage error (MAPE), calculated as:
$$ \text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i – \hat{y}_i)^2} $$
$$ \text{MAPE} = \frac{100\%}{n} \sum_{i=1}^{n} \left| \frac{y_i – \hat{y}_i}{y_i} \right| $$
where \( y_i \) is the actual value, \( \hat{y}_i \) is the predicted value, and \( n \) is the number of samples. Lower values indicate better prediction accuracy. I compare MCNN-LSTM against baseline models like standalone CNN and LSTM. The results show that increasing the window length improves performance, with \( W = 80 \) yielding the best outcomes. For cycle life prediction, the MCNN-LSTM achieves RMSE below 30 cycles and MAPE below 2% on the test set, demonstrating high precision even with only about 6% of the total lifespan data (assuming an average li ion battery life of 1500 cycles). This underscores the model’s ability to extract meaningful degradation features early on.
To predict knee points, I first establish a strong linear relationship between knee point occurrence and total cycle life across the dataset. Let \( y_{\text{knee}} \) denote the knee point cycle and \( y_{\text{life}} \) the total cycle life. A linear regression fit gives:
$$ y_{\text{knee}} = 1.2319 \, y_{\text{life}} – 8.1257 $$
with a coefficient of determination \( R^2 = 0.9841 \). This high correlation allows the same MCNN-LSTM model, trained for cycle life prediction, to be extended for knee point forecasting by applying the linear transformation. Experiments repeated 10 times confirm robust predictions, with RMSE below 60 cycles and MAPE below 5% for knee points. The consistency across runs highlights the model’s stability and generalizability for li ion battery health monitoring.
The following table summarizes the prediction errors for different models at \( W = 80 \), illustrating the superiority of the multi-scale fusion approach:
| Model | RMSE (Cycles) – Test Set | MAPE (%) – Test Set |
|---|---|---|
| LSTM | 133 | 10.19 |
| CNN | 78 | 7.12 |
| MCNN-LSTM | 23 | 1.26 |
Additionally, the table below provides examples of charging protocols and corresponding cycle lives from the dataset, emphasizing the variability in li ion battery aging:
| Charging Protocol | Cycle Life (Examples) |
|---|---|
| 5C (67%)-4C | 813, 825, 1009, 1046, 1935 |
| 5.6C (19%)-4.6C | 817, 796, 1267, 1048, 1146, 1028, 1093 |
| 5.6C (36%)-4.3C | 1115, 828, 932, 858, 850, 923 |
| 3.7C (31%)-5.9C | 541, 667, 772 |
| 5.3C (54%)-4C | 1315, 1158, 1039, 989, 935, 940 |
These results validate the effectiveness of automatic feature learning in capturing complex degradation patterns. The MCNN-LSTM model eliminates the need for manual HI design, reducing subjectivity and computational overhead. By processing raw V/I/T data, it adapts to diverse operating conditions, making it suitable for real-world applications where li ion batteries undergo varying stress factors. Moreover, the early prediction of knee points enables proactive maintenance, such as adjusting charging strategies or replacing batteries before accelerated decay compromises safety.
In conclusion, I have developed a multi-scale feature fusion model for predicting both cycle life and knee points in li ion batteries. The MCNN-LSTM architecture leverages dilated CNNs and LSTMs to extract temporal features at multiple scales, enhancing prediction accuracy with minimal early-cycle data. Experimental results on a public dataset confirm that the model outperforms conventional methods, with errors below 30 cycles for life prediction and 60 cycles for knee points. This work contributes to advanced battery management systems by providing a data-driven tool for early degradation assessment. Future directions include extending the model to online learning scenarios, incorporating additional sensor data (e.g., impedance), and testing on other li ion battery chemistries to further improve robustness and applicability in diverse energy storage systems.